On weak-strong uniqueness and singular limit for the compressible Primitive Equations

Abstract

This paper addresses the weak-strong uniqueness property and singular limit for the compressible Primitive Equations (PE). We show that a weak solution coincides with the strong solution emanating from the same initial data. On the other hand, we prove compressible PE will approach the incompressible inviscid PE equations in the regime of low Mach number and large Reynolds number in the case of well-prepared initial data. To the best of the authors' knowledge, this is the first work to bridge the link between the compressible PE with incompressible inviscid PE.

References in corpus (11)

• Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system
• Existence of Global Weak Solutions for 3D Degenerate Compressible Navier-Stokes Equations
• Local Martingale and Pathwise Solutions for an Abstract Fluids Model
• Weak-strong uniqueness for the isentropic compressible Navier-Stokes system
• Local and Global Well-posedness of Strong Solutions to the 3D Primitive Equations with Vertical Eddy Diffusivity
• Global Existence and Regularity for the 3D Stochastic Primitive Equations of the Ocean and Atmosphere with Multiplicative White Noise
• Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
• Compressible primitive equation: formal derivation and stability of weak solutions
• Dynamic Transitions and Baroclinic Instability for 3D Continuously Stratified Boussinesq Flows
• Global weak solutions to 3D compressible Primitive equations with density-dependent viscosity
• Global Existence of Weak Solutions to the Compressible Primitive Equations of Atmospheric Dynamics with Degenerate Viscosities